SIMI VALLEY, California (CNN) -- Front-runner Rudy Giuliani broke with the other nine Republicans in the party's first debate of the presidential campaign, saying that it would be OK if the Supreme Court overturned its ruling on abortion rights but that he respected a woman's right to choose.

"I hate abortion" and encourage adoption, the former New York City mayor said later in the debate. But he added that he "would respect a woman's right to make a different choice."

During the debate, which was held at the late president's library with his widow, Nancy, looking on, the GOP hopefuls invoked his name 19 times.

"What we can borrow from Ronald Reagan ... is that great sense of optimism," said Giuliani.

"Ronald Reagan was a president of strength," said former Massachusetts Gov. Mitt Romney.

However, most of the candidates refused to embrace one of Nancy Reagan's pet causes: embryonic stem cell research.

Only two candidates, Giuliani and Arizona Sen. John McCain, suggested they would support expanding federal funding for such research.

"This is a tough issue for those us in the pro-life community. ... We need to do what we can to relieve human suffering," McCain said.

Giuliani said, "As long as we're not creating life in order to destroy it, as long as we're not having human cloning ... there is plenty of opportunity to then use federal funds."

The GOP field was largely dismissive of Democratic calls for withdrawing troops from Iraq, but some of the candidates were critical of the war's execution.

"Clearly, there was a real error in judgment, and that primarily had to do with listening to a lot of folks who were civilians in suits and silk ties and not listing enough to the generals with mud and blood on their boots," Huckabee said.

However, he said, "it's important that we finish the job, that we do it right, rather than have to go back and some day do it over," he said.

McCain reiterated his optimism that Bush's latest initiative in Iraq, which involves increasing troop strength to try to get a handle on the violence, was working.

"[The war] was badly mismanaged for four years, but we have a new strategy that I think and pray every night will succeed," he said.

But Texas Rep. Ron Paul -- who has opposed the war from the beginning and voted against it -- was alone in calling on the GOP to return to a "non-interventionist" foreign policy, which he said was "the traditional American foreign policy and the Republican foreign policy."

Salute to bipartisanship draws rebuke

The candidates rarely mentioned Bush, but near the end of the debate, Giuliani offered the night's most effusive praise of the current commander-in-chief.

"On September 11, 2001, we thought we were going to be attacked many, many times between then and now. We haven't been," Giuliani said, lauding Bush's decision "to put us on offense against terrorists."

Thursday's 90-minute debate, sponsored by MSNBC and The Politico, was the first chance to see a side-by-side campaign performance by McCain and Giuliani, the two front-runners in the polls. Both men sought to use their experience and cross-party appeal to argue their candidacy.

"I may not be the youngest candidate in this race, but I'm the most prepared," said McCain, 70.

"I know how the world works. I know the good and evil in it. I've seen it," said McCain, a former prisoner of war in Vietnam.

Giuliani touted his record leading heavily Democratic New York, where he "reduced crime, reduced welfare, balanced the budget, lowered taxes 23 times."

"If we're going to win, and we're going to govern after we win, we have to reach out, bring in Democrats, bring in independents," he said.

That salute to bipartisanship drew a retort from Colorado Rep. Tom Tancredo, who noted that "we're standing in a place dedicated to a man who we would not call a centrist."

"He was also able to win the presidency, twice. Why? Because he believed in principles, he articulated them and he put them into effect."

Democratic National Committee Chairman Howard Dean told The Associated Press the debate "confirms that a Democrat will be elected in 2008. The Republican presidential contenders are only offering more of the same failed leadership and misplaced priorities that President Bush brought to the White House."

Romney: 'I changed my mind'

Romney, hoping to crack into the top tier after raising an impressive $21 million in the first quarter of the year, was called on to directly address his changed stance on abortion rights.

"I've always been personally pro-life, but, for me, it was a great question about whether or not government should intrude in that decision. And when I ran for office [in Massachusetts], I said I'd protect the law as it was, which is effectively a pro-choice position," he said.

Romney said he changed his mind after the state began studying cloning about two years ago.

"I took the same course that Ronald Reagan and George Herbert Walker Bush" took, he said.

Romney was asked by moderator Chris Matthews what he would say to Roman Catholic bishops who would deny communion to elected officials who support abortion rights.

"I don't say anything to Roman Catholic bishops," said Romney, who is Mormon. "They can do whatever the heck they want."

Giuliani is one of those Catholic politicians who supports abortion rights, to the dismay of many social conservatives in the GOP base.

He reiterated Thursday that if elected, he would not try to lift a ban on using federal funds for abortions for poor women, something he advocated as mayor.

While many of the other candidates responded enthusiastically in the affirmative when asked if it would be a good day for America if the Supreme Court overturned Roe vs. Wade, the 1973 decision legalizing abortion.

"It would be OK to repeal," he said, adding that it would also be OK "if a strict constructionist judge viewed it as precedent."

Also taking part in the debate were Sen. Sam Brownback of Kansas; Rep. Duncan Hunter of California; and three former governors, Mike Huckabee of Arkansas, Tommy Thompson of Wisconsin and Jim Gilmore of Virginia.

Two Republicans who are considering a presidential bid but have not yet announced -- former Sen. Fred Thompson of Tennessee and former House Speaker Newt Gingrich of Georgia -- did not participate.

The latest CNN/Opinion Research Corp. poll, conducted in mid-April, found that Giuliani was the choice of 27 percent of registered Republicans, compared with 24 percent for McCain, a margin that was within the sampling error of plus or minus 5 percentage points.

Thompson was the choice of 11 percent, followed by Romney at 10 percent and Gingrich at 8 percent. The other candidates were all at 2 percent or less, and 13 percent of registered Republicans said they were unsure who they would back.

The state where Thursday's debate was held, California, will take on new importance in the nominating process next year, after state legislators voted to move up the primary from June to February 5.